Chiral Effective Field Theory of the resonance MDM

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Chiral Effective Field Theory of the ?-resonance
MDM

• Vladimir Pascalutsa
• Physics Department, The College of William
  Mary
• and
• Theory Center, Jefferson Laboratory

Supported by
_at_ Coll. Meeting EM properties of the
Delta-resonance Trento, Italy, Oct 16-19, 2006
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Low-energy QCD in the presence of resonances
Weinberg (1979), Gasser Leutwyler (1984),
Low-energy QCD ChPT
Lagrangian
S-matrix
However, near a resonance (or a bound state)
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Chiral Lagrangians with ? and power counting
Include the ? as an explicit d.o.f. ,
Jenkins Manohar
(1991), described by a spin-3/2
(Rarita-Schwinger) isospin-3/2 (isoquartet) field
Review V.P., Vanderhaeghen S.-N
Yang, hep-ph/0609004 (to appear Phys Rept)
Power counting
Jenkins Manohar (1991), Hemmert et al. (1998)
(2006)
N and ? propagators
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? expansion
V.P. Phillips, PRC (2003), see also Hanhart
Kaiser, PRC (2003) NN? Van Kolck (2003) halo
nuclei
c.f., SN 1/p O(1/?)
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Pion-nucleon scattering in the resonance region
Renormalized NLO propagator
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?(1232) magnetic moment ?? from Radiative Pion
Photoproduction (?N -gt Np ? )
V.P. Vanderhaeghen, PRL 94 (2005)
Calculation to NLO in the d expansion 2 free LECs
?(s) and m(v)

• First observations of the magnetic moment of a
  strongly unstable particle.
• High-precision experiment at MAMI (Mainz) using
  Crystal Ball and TAPS detectors. completed 2005,
  analysis in progress.
• Theory input needed

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LECs loops
electric charge
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Pion-mass dependence of magnetic moments
(quenched) Lattice QCD Leinweber
(1992) Cloet,Leinweber,Thomas (2003) Lee et.al.
(2004) revised (2006)
Chiral EFT (? expansion NLO)
Interpretation of the im. part of the MDM B.R.
Holstein won Absolute Prize! (1L) Increase/dec
rease (depending on the spin orientation) of
width in an external magnetic field (B), ?? ?
Im? B.
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?? from ? p -gt p p0 ? observables
Data points from an older expt Kotulla et al.,
TAPS_at_MAMI 2002
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• p ? ? p0 p doubly polarized cross sections